• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.619-627
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• 2002

It is unpractical for the optimal design theory based on the given model and assumption to be applied to the real-world experimentation. Particularly, when the experimenter feels it necessary to consider multiple objectives in experimentation, its modified version of optimality criteria is indeed desired. The constrained optimal design is one of many methods developed in this context. But when the number of constraints exceeds two, there always exists a problem in specifying the lower limit for the efficiencies of the constraints because the “infeasible solution” issue arises very quickly. In this paper, we developed a sequential approach to tackle this problem assuming that all the constraints can be ranked in terms of importance. This approach has been applied to the polynomial regression model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권1호
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• pp.1-15
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• 2014

We have investigated optimal control strategies for prevention of ecstasy use. Ecstasy use has continued at raves and nightclubs in recent years and the reduction of ecstasy use has become one of the important issues in society. We apply optimal control theory to a model of the peer-driven dynamics of ecstasy use. Our goal is to minimize the ecstasy use class and the intervention cost. Optimal control is characterized in terms of the solution of optimality system, which is the state system coupled with the adjoint system and the optimality equations. The numerical simulations show the optimal prevention policies of ecstasy use in various scenarios.

• Communications for Statistical Applications and Methods
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• 제24권2호
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• pp.129-142
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• 2017

In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.

• International Journal of Reliability and Applications
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• 제18권2호
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• pp.45-63
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• 2017

In this paper, we have formulated optimum Accelerated Life Test (ALT) plan for a parallel system with two independent components using masked data with ramp-stress loading scheme and Type-I censoring. Consider a system of two independent and non-identical components connected in parallel. Such a system fails whenever all of its components has failed. The exact component that causes the system to fail is often unknown due to cost and time constraint. For each parallel system at test, we observe its system's failure time and a set of component that includes the component actually causing the system to fail. The stress-life relationship is modelled using inverse power law, and cumulative exposure model is assumed to model the effect of changing stress. The optimal plan consists in finding out the optimum stress rate using D-optimality criterion. The method developed has been explained using a numerical example and sensitivity analysis carried out.

• Structural Engineering and Mechanics
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• 제83권4호
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• pp.537-549
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• 2022

In this paper, a novel multi-feature model predictive control (MPC) framework with real-time and adaptive performances is proposed for intelligent structural control in which some drawbacks of the algorithm including, complex control rule and non-optimality, are alleviated. Hence, Linear Programming (LP) is utilized to simplify the resulted control rule. Afterward, the Whale Optimization Algorithm (WOA) is applied to the optimal and adaptive tuning of the LP weights independently at each time step. The stochastic control rule is also achieved using Kalman Filter (KF) to handle noisy measurements. The Extreme Learning Machine (ELM) is then adopted to develop a data-driven and real-time control algorithm. The efficiency of the developed algorithm is then demonstrated by numerical simulation of a twenty-story high-rise benchmark building subjected to earthquake excitations. The competency of the proposed method is proven from the aspects of optimality, stochasticity, and adaptivity compared to the KF-based MPC (KMPC) and constrained MPC (CMPC) algorithms in vibration suppression of building structures. The average value for performance indices in the near-field and far-field (El earthquakes demonstrates a reduction up to 38.3% and 32.5% compared with KMPC and CMPC, respectively.

• International Journal of Reliability and Applications
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• 제12권2호
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• pp.117-122
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• 2011

In this paper, we suggest the optimal replacement policy following the expiration of repair warranty when the cost of minimal repair depends on the age of system. To do so, we first explain the replacement model under repair warranty. And then the optimal replacement policy following the expiration of repair warranty is discussed from the user's point of view. The criterion used to determine the optimality of the replacement model is the expected cost rate per unit time, which is obtained from the expected cycle length and the expected total cost for our replacement model. The numerical examples are given for illustrative purpose.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2006년도 추계학술대회
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• pp.531-534
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• 2006

Response surface methodology (RSM) is a useful collection of experimentation techniques for developing, improving, and optimizing products and processes. When we are to estimate second-order regression model and optimize quality characteristic by RSM, central composite designs and Box-Behnken designs are widely in use. However, in developing cutting-edge products, it is very crucial to reduce the time of experimentation as much as possible. In this paper small-sized second-order designs are introduced and their estimation abilities are compared in terms of D-optimality, A-optimality, and variance of regression coefficients, ease of experimentation, number of experiments. Then we present a guideline of using specific designs for specific experimentation circumstances. The result of this study will be beneficial to experimenters who face experiments which are expensive, difficult, or time-consuming.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2006년도 춘계공동학술대회 논문집
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• pp.1085-1092
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• 2006

Response surface methodology(RSM) is a useful collection of experimentation techniques for developing, improving, and optimizing products and processes. When we are to estimate second-order regression model and optimize quality characteristic by RSM, central composite designs and Box-Behnken designs are widely in use. However, in developing cutting-edge products, it is very crucial to reduce the time of experimentation as much as possible. In this paper small-sized second-order designs are introduced and their estimation abilities are compared in terms of D-optimality, A-optimality, and variance of regression coefficients. The result of this study will be beneficial to experimenters who face experiments which are expensive, difficult, or time-consuming.

• Korean Chemical Engineering Research
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• 제51권1호
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• pp.87-92
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• 2013

미세조류는 바이오연료를 생산하기 위해 필요한 성분인 지방질의 생산성이 우수하기 때문에 바이오연료의 유망한 원료로서 최근 많은 주목을 받고 있다. 본 연구에서는, 이러한 미세조류의 성장 속도와 미세조류 내부의 지방의 함량이 최대가 되도록 하기 위한 목적으로, 미세조류의 성장과 지방의 생성을 설명하는 제일원리(first principle)에 근거한 상미분방정식(ODE) 모델에 대하여 조사하였다. 모델은 6개의 상태변수와 12개의 파라미터로 이루어져 있으며, 미세조류의 성장을 영양분의 흡수와 흡수된 영양분에 의한 성장으로 두 단계로 나누어 설명한 Droop 모델의 가정을 따른다. 본 연구에서는 민감도 분석(Sensitivity analysis)을 위한 최대의 정보를 줄 수 있는 입력 신호를 결정하기 위해 D-optimality criterion을 이용한 최적 입력 설계(Optimal input design)를 수행하였으며, 구하여진 입력 신호를 적용하여 민감도 분석을 수행하여 모델에 좀 더 중요한 파라미터를 결정하였다. 또한 미세조류의 성장속도와 지방의 함량이 최대가 되도록 하기 위하여 모델 예측 제어(MPC)를 수행하였다.

• 응용통계연구
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• 제28권3호
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• pp.561-571
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• 2015

실험영역을 벗어나는 점에 해당하는 반응값 예측을 위한 최적실험을 고려할 때 실험에 필요한 받힘점을 위한 실험기준을 선택하는 경우 매우 신중하여야 한다. 왜냐하면 가정한 모형과 오차구도가 실험영역을 벗어나도 타당하다는 가정을 하여야 되기 때문이다. 따라서 기존문헌의 외삽최적의 실험기준을 이러한 상황에 맞게 설계될 수 있도록 수정하였다. 본 연구에서는 maximin방법을 적용하여 새로운 실험기준의 특징 및 강건성을 단순회귀모형과 이차회귀모형을 기준으로 검정하였다.